Daily Papers

Large Language Models (LLMs) rely on safety alignment to produce socially acceptable responses. This is typically achieved through instruction tuning and reinforcement learning from human feedback. However, this alignment is known to be brittle: further fine-tuning, even on benign or lightly contaminated data, can degrade safety and reintroduce harmful behaviors. A growing body of work suggests that alignment may correspond to identifiable geometric directions in weight space, forming subspaces that could, in principle, be isolated or preserved to defend against misalignment. In this work, we conduct a comprehensive empirical study of this geometric perspective. We examine whether safety-relevant behavior is concentrated in specific subspaces, whether it can be separated from general-purpose learning, and whether harmfulness arises from distinguishable patterns in internal representations. Across both parameter and activation space, our findings are consistent: subspaces that amplify safe behaviors also amplify unsafe ones, and prompts with different safety implications activate overlapping representations. We find no evidence of a subspace that selectively governs safety. These results challenge the assumption that alignment is geometrically localized. Rather than residing in distinct directions, safety appears to emerge from entangled, high-impact components of the model's broader learning dynamics. This suggests that subspace-based defenses may face fundamental limitations and underscores the need for alternative strategies to preserve alignment under continued training. We corroborate these findings through multiple experiments on five open-source LLMs. Our code is publicly available at: https://github.com/CERT-Lab/safety-subspaces.

Modern large language models (LLMs) employ various forms of logical inference, both implicitly and explicitly, when addressing reasoning tasks. Understanding how to optimally leverage these inference paradigms is critical for advancing LLMs' reasoning capabilities. This paper adopts an exploratory approach by introducing a controlled evaluation environment for analogical reasoning -- a fundamental cognitive task -- that is systematically parameterized across three dimensions: modality (textual, visual, symbolic), difficulty (easy, medium, hard), and task format (multiple-choice or free-text generation). We analyze the comparative dynamics of inductive, abductive, and deductive inference pipelines across these dimensions, and demonstrate that our findings generalize to broader in-context learning tasks. Additionally, we investigate advanced paradigms such as hypothesis selection, verification, and refinement, revealing their potential to scale up logical inference in LLM reasoning. This exploratory study provides a foundation for future research in enhancing LLM reasoning through systematic logical inference strategies.

We present DrivAerNet++, the largest and most comprehensive multimodal dataset for aerodynamic car design. DrivAerNet++ comprises 8,000 diverse car designs modeled with high-fidelity computational fluid dynamics (CFD) simulations. The dataset includes diverse car configurations such as fastback, notchback, and estateback, with different underbody and wheel designs to represent both internal combustion engines and electric vehicles. Each entry in the dataset features detailed 3D meshes, parametric models, aerodynamic coefficients, and extensive flow and surface field data, along with segmented parts for car classification and point cloud data. This dataset supports a wide array of machine learning applications including data-driven design optimization, generative modeling, surrogate model training, CFD simulation acceleration, and geometric classification. With more than 39 TB of publicly available engineering data, DrivAerNet++ fills a significant gap in available resources, providing high-quality, diverse data to enhance model training, promote generalization, and accelerate automotive design processes. Along with rigorous dataset validation, we also provide ML benchmarking results on the task of aerodynamic drag prediction, showcasing the breadth of applications supported by our dataset. This dataset is set to significantly impact automotive design and broader engineering disciplines by fostering innovation and improving the fidelity of aerodynamic evaluations.

We study how multi-head softmax attention models are trained to perform in-context learning on linear data. Through extensive empirical experiments and rigorous theoretical analysis, we demystify the emergence of elegant attention patterns: a diagonal and homogeneous pattern in the key-query (KQ) weights, and a last-entry-only and zero-sum pattern in the output-value (OV) weights. Remarkably, these patterns consistently appear from gradient-based training starting from random initialization. Our analysis reveals that such emergent structures enable multi-head attention to approximately implement a debiased gradient descent predictor -- one that outperforms single-head attention and nearly achieves Bayesian optimality up to proportional factor. Furthermore, compared to linear transformers, the softmax attention readily generalizes to sequences longer than those seen during training. We also extend our study to scenarios with non-isotropic covariates and multi-task linear regression. In the former, multi-head attention learns to implement a form of pre-conditioned gradient descent. In the latter, we uncover an intriguing regime where the interplay between head number and task number triggers a superposition phenomenon that efficiently resolves multi-task in-context learning. Our results reveal that in-context learning ability emerges from the trained transformer as an aggregated effect of its architecture and the underlying data distribution, paving the way for deeper understanding and broader applications of in-context learning.

Operational forecasting of the ionosphere remains a critical space weather challenge due to sparse observations, complex coupling across geospatial layers, and a growing need for timely, accurate predictions that support Global Navigation Satellite System (GNSS), communications, aviation safety, as well as satellite operations. As part of the 2025 NASA Heliolab, we present a curated, open-access dataset that integrates diverse ionospheric and heliospheric measurements into a coherent, machine learning-ready structure, designed specifically to support next-generation forecasting models and address gaps in current operational frameworks. Our workflow integrates a large selection of data sources comprising Solar Dynamic Observatory data, solar irradiance indices (F10.7), solar wind parameters (velocity and interplanetary magnetic field), geomagnetic activity indices (Kp, AE, SYM-H), and NASA JPL's Global Ionospheric Maps of Total Electron Content (GIM-TEC). We also implement geospatially sparse data such as the TEC derived from the World-Wide GNSS Receiver Network and crowdsourced Android smartphone measurements. This novel heterogeneous dataset is temporally and spatially aligned into a single, modular data structure that supports both physical and data-driven modeling. Leveraging this dataset, we train and benchmark several spatiotemporal machine learning architectures for forecasting vertical TEC under both quiet and geomagnetically active conditions. This work presents an extensive dataset and modeling pipeline that enables exploration of not only ionospheric dynamics but also broader Sun-Earth interactions, supporting both scientific inquiry and operational forecasting efforts.

Deep learning models for natural language processing (NLP) are increasingly adopted and deployed by analysts without formal training in NLP or machine learning (ML). However, the documentation intended to convey the model's details and appropriate use is tailored primarily to individuals with ML or NLP expertise. To address this gap, we conduct a design inquiry into interactive model cards, which augment traditionally static model cards with affordances for exploring model documentation and interacting with the models themselves. Our investigation consists of an initial conceptual study with experts in ML, NLP, and AI Ethics, followed by a separate evaluative study with non-expert analysts who use ML models in their work. Using a semi-structured interview format coupled with a think-aloud protocol, we collected feedback from a total of 30 participants who engaged with different versions of standard and interactive model cards. Through a thematic analysis of the collected data, we identified several conceptual dimensions that summarize the strengths and limitations of standard and interactive model cards, including: stakeholders; design; guidance; understandability & interpretability; sensemaking & skepticism; and trust & safety. Our findings demonstrate the importance of carefully considered design and interactivity for orienting and supporting non-expert analysts using deep learning models, along with a need for consideration of broader sociotechnical contexts and organizational dynamics. We have also identified design elements, such as language, visual cues, and warnings, among others, that support interactivity and make non-interactive content accessible. We summarize our findings as design guidelines and discuss their implications for a human-centered approach towards AI/ML documentation.

Learning dynamics, which describes how the learning of specific training examples influences the model's predictions on other examples, gives us a powerful tool for understanding the behavior of deep learning systems. We study the learning dynamics of large language models during different types of finetuning, by analyzing the step-wise decomposition of how influence accumulates among different potential responses. Our framework allows a uniform interpretation of many interesting observations about the training of popular algorithms for both instruction tuning and preference tuning. In particular, we propose a hypothetical explanation of why specific types of hallucination are strengthened after finetuning, e.g., the model might use phrases or facts in the response for question B to answer question A, or the model might keep repeating similar simple phrases when generating responses. We also extend our framework and highlight a unique "squeezing effect" to explain a previously observed phenomenon in off-policy direct preference optimization (DPO), where running DPO for too long makes even the desired outputs less likely. This framework also provides insights into where the benefits of on-policy DPO and other variants come from. The analysis not only provides a novel perspective of understanding LLM's finetuning but also inspires a simple, effective method to improve alignment performance.

Diffusion models have achieved remarkable success across a wide range of generative tasks. A key challenge is understanding the mechanisms that prevent their memorization of training data and allow generalization. In this work, we investigate the role of the training dynamics in the transition from generalization to memorization. Through extensive experiments and theoretical analysis, we identify two distinct timescales: an early time τ_gen at which models begin to generate high-quality samples, and a later time τ_mem beyond which memorization emerges. Crucially, we find that τ_mem increases linearly with the training set size n, while τ_gen remains constant. This creates a growing window of training times with n where models generalize effectively, despite showing strong memorization if training continues beyond it. It is only when n becomes larger than a model-dependent threshold that overfitting disappears at infinite training times. These findings reveal a form of implicit dynamical regularization in the training dynamics, which allow to avoid memorization even in highly overparameterized settings. Our results are supported by numerical experiments with standard U-Net architectures on realistic and synthetic datasets, and by a theoretical analysis using a tractable random features model studied in the high-dimensional limit.

Learning a precise dynamics model can be crucial for offline reinforcement learning, which, unfortunately, has been found to be quite challenging. Dynamics models that are learned by fitting historical transitions often struggle to generalize to unseen transitions. In this study, we identify a hidden but pivotal factor termed dynamics reward that remains consistent across transitions, offering a pathway to better generalization. Therefore, we propose the idea of reward-consistent dynamics models: any trajectory generated by the dynamics model should maximize the dynamics reward derived from the data. We implement this idea as the MOREC (Model-based Offline reinforcement learning with Reward Consistency) method, which can be seamlessly integrated into previous offline model-based reinforcement learning (MBRL) methods. MOREC learns a generalizable dynamics reward function from offline data, which is subsequently employed as a transition filter in any offline MBRL method: when generating transitions, the dynamics model generates a batch of transitions and selects the one with the highest dynamics reward value. On a synthetic task, we visualize that MOREC has a strong generalization ability and can surprisingly recover some distant unseen transitions. On 21 offline tasks in D4RL and NeoRL benchmarks, MOREC improves the previous state-of-the-art performance by a significant margin, i.e., 4.6% on D4RL tasks and 25.9% on NeoRL tasks. Notably, MOREC is the first method that can achieve above 95% online RL performance in 6 out of 12 D4RL tasks and 3 out of 9 NeoRL tasks.

Grokking, i.e., test performance keeps improving long after training loss converged, has been recently witnessed in neural network training, making the mechanism of generalization and other emerging capabilities such as reasoning mysterious. While prior studies usually train small models on a few toy or highly-specific tasks for thousands of epochs, we conduct the first study of grokking on checkpoints during one-pass pretraining of a 7B large language model (LLM), i.e., OLMoE. We compute the training loss and evaluate generalization on diverse benchmark tasks, including math reasoning, code generation, and commonsense/domain-specific knowledge retrieval tasks. Our study, for the first time, verifies that grokking still happens in the pretraining of large-scale foundation models, though different data may enter grokking stages asynchronously. We further demystify grokking's "emergence of generalization" by investigating LLM internal dynamics. Specifically, we find that training samples' pathways (i.e., expert choices across layers) evolve from random, instance-specific to more structured and shareable between samples during grokking. Also, the complexity of a sample's pathway reduces despite the converged loss. These indicate a memorization-to-generalization conversion, providing a mechanistic explanation of delayed generalization. In the study, we develop two novel metrics to quantify pathway distance and the complexity of a single pathway. We show their ability to predict the generalization improvement on diverse downstream tasks. They are efficient, simple to compute and solely dependent on training data. Hence, they have practical value for pretraining, enabling us to monitor the generalization performance without finetuning and test. Theoretically, we show that more structured pathways reduce model complexity and improve the generalization bound.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a model learns, the order in which it learns them, and its ability to manipulate those concepts? To address these questions, we propose analyzing a model's learning dynamics via a framework we call the concept space, where each axis represents an independent concept underlying the data generating process. By characterizing learning dynamics in this space, we identify how the speed at which a concept is learned, and hence the order of concept learning, is controlled by properties of the data we term concept signal. Further, we observe moments of sudden turns in the direction of a model's learning dynamics in concept space. Surprisingly, these points precisely correspond to the emergence of hidden capabilities, i.e., where latent interventions show the model possesses the capability to manipulate a concept, but these capabilities cannot yet be elicited via naive input prompting. While our results focus on synthetically defined toy datasets, we hypothesize a general claim on emergence of hidden capabilities may hold: generative models possess latent capabilities that emerge suddenly and consistently during training, though a model might not exhibit these capabilities under naive input prompting.

Cognitive dynamics are pivotal to advance human understanding of the world. Recent advancements in large language models (LLMs) reveal their potential for cognitive simulation. However, these LLM-based cognitive studies primarily focus on static modeling, overlooking the dynamic nature of cognition. To bridge this gap, we propose the concept of the cognitive dynamics of LLMs and present a corresponding task with the inspiration of longitudinal studies. Towards the task, we develop CogBench, a novel benchmark to assess the cognitive dynamics of LLMs and validate it through participant surveys. We also design two evaluation metrics for CogBench, including Authenticity and Rationality. Recognizing the inherent static nature of LLMs, we introduce CogGPT for the task, which features an innovative iterative cognitive mechanism aimed at enhancing lifelong cognitive dynamics. Empirical results demonstrate the superiority of CogGPT over existing methods, particularly in its ability to facilitate role-specific cognitive dynamics under continuous information flows.

Reinforcement learning (RL) has demonstrated significant success in enhancing reasoning capabilities in large language models (LLMs). One of the most widely used RL methods is Group Relative Policy Optimization (GRPO)~Shao-2024-Deepseekmath, known for its memory efficiency and success in training DeepSeek-R1~Guo-2025-Deepseek. However, GRPO stalls when all sampled responses in a group are incorrect -- referred to as an all-negative-sample group -- as it fails to update the policy, hindering learning progress. The contributions of this paper are two-fold. First, we propose a simple yet effective framework that introduces response diversity within all-negative-sample groups in GRPO using AI feedback. We also provide a theoretical analysis, via a stylized model, showing how this diversification improves learning dynamics. Second, we empirically validate our approach, showing the improved performance across various model sizes (7B, 14B, 32B) in both offline and online learning settings with 10 benchmarks, including base and distilled variants. Our findings highlight that learning from all-negative-sample groups is not only feasible but beneficial, advancing recent insights from Xiong-2025-Minimalist.

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension phase), leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.

Large language models accumulate vast knowledge during pre-training, yet the dynamics governing this acquisition remain poorly understood. This work investigates the learning dynamics of language models on a synthetic factual recall task, uncovering three key findings: First, language models learn in three phases, exhibiting a performance plateau before acquiring precise factual knowledge. Mechanistically, this plateau coincides with the formation of attention-based circuits that support recall. Second, the training data distribution significantly impacts learning dynamics, as imbalanced distributions lead to shorter plateaus. Finally, hallucinations emerge simultaneously with knowledge, and integrating new knowledge into the model through fine-tuning is challenging, as it quickly corrupts its existing parametric memories. Our results emphasize the importance of data distribution in knowledge acquisition and suggest novel data scheduling strategies to accelerate neural network training.

Large language models (LLMs) have been increasingly applied to tasks in language understanding and interactive decision-making, with their impressive performance largely attributed to the extensive domain knowledge embedded within them. However, the depth and breadth of this knowledge can vary across domains. Many existing approaches assume that LLMs possess a comprehensive understanding of their environment, often overlooking potential gaps in their grasp of actual world dynamics. To address this, we introduce Discover, Verify, and Evolve (DiVE), a framework that discovers world dynamics from a small number of demonstrations, verifies the accuracy of these dynamics, and evolves new, advanced dynamics tailored to the current situation. Through extensive evaluations, we assess the impact of each component on performance and compare the dynamics generated by DiVE to human-annotated dynamics. Our results show that LLMs guided by DiVE make more informed decisions, achieving rewards comparable to human players in the Crafter environment and surpassing methods that require prior task-specific training in the MiniHack environment.

When do machine learning systems fail to generalize, and what mechanisms could improve their generalization? Here, we draw inspiration from cognitive science to argue that one weakness of machine learning systems is their failure to exhibit latent learning -- learning information that is not relevant to the task at hand, but that might be useful in a future task. We show how this perspective links failures ranging from the reversal curse in language modeling to new findings on agent-based navigation. We then highlight how cognitive science points to episodic memory as a potential part of the solution to these issues. Correspondingly, we show that a system with an oracle retrieval mechanism can use learning experiences more flexibly to generalize better across many of these challenges. We also identify some of the essential components for effectively using retrieval, including the importance of within-example in-context learning for acquiring the ability to use information across retrieved examples. In summary, our results illustrate one possible contributor to the relative data inefficiency of current machine learning systems compared to natural intelligence, and help to understand how retrieval methods can complement parametric learning to improve generalization.

Despite exceptional capabilities in knowledge-intensive tasks, Large Language Models (LLMs) face a critical gap in understanding how they internalize new knowledge, particularly how to structurally embed acquired knowledge in their neural computations. We address this issue through the lens of knowledge circuit evolution, identifying computational subgraphs that facilitate knowledge storage and processing. Our systematic analysis of circuit evolution throughout continual pre-training reveals several key findings: (1) the acquisition of new knowledge is influenced by its relevance to pre-existing knowledge; (2) the evolution of knowledge circuits exhibits a distinct phase shift from formation to optimization; (3) the evolution of knowledge circuits follows a deep-to-shallow pattern. These insights not only advance our theoretical understanding of the mechanisms of new knowledge acquisition in LLMs, but also provide potential implications for improving continual pre-training strategies to enhance model performance. Code and data will be available at https://github.com/zjunlp/DynamicKnowledgeCircuits.

While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which conditions it happens, and is closely related to the gradient dynamics of the training, for complex structured inputs. We propose a novel framework, named Li_2, that captures three key stages for the grokking behavior of 2-layer nonlinear networks: (I) \textbf{L}azy learning, (II) \textbf{i}ndependent feature learning and (III) \textbf{i}nteractive feature learning. At the lazy learning stage, top layer overfits to random hidden representation and the model appears to memorize. Thanks to lazy learning and weight decay, the backpropagated gradient G_F from the top layer now carries information about the target label, with a specific structure that enables each hidden node to learn their representation independently. Interestingly, the independent dynamics follows exactly the gradient ascent of an energy function E, and its local maxima are precisely the emerging features. We study whether these local-optima induced features are generalizable, their representation power, and how they change on sample size, in group arithmetic tasks. When hidden nodes start to interact in the later stage of learning, we provably show how G_F changes to focus on missing features that need to be learned. Our study sheds lights on roles played by key hyperparameters such as weight decay, learning rate and sample sizes in grokking, leads to provable scaling laws of feature emergence, memorization and generalization, and reveals the underlying cause why recent optimizers such as Muon can be effective, from the first principles of gradient dynamics. Our analysis can be extended to multi-layer architectures.

Prompting Large Language Models (LLMs), or providing context on the expected model of operation, is an effective way to steer the outputs of such models to satisfy human desiderata after they have been trained. But in rapidly evolving domains, there is often need to fine-tune LLMs to improve either the kind of knowledge in their memory or their abilities to perform open ended reasoning in new domains. When human's learn new concepts, we often do so by linking the new material that we are studying to concepts we have already learned before. To that end, we ask, "can prompting help us teach LLMs how to learn". In this work, we study a novel generalization of instruction tuning, called contextual fine-tuning, to fine-tune LLMs. Our method leverages instructional prompts designed to mimic human cognitive strategies in learning and problem-solving to guide the learning process during training, aiming to improve the model's interpretation and understanding of domain-specific knowledge. We empirically demonstrate that this simple yet effective modification improves the ability of LLMs to be fine-tuned rapidly on new datasets both within the medical and financial domains.

To cope with real-world dynamics, an intelligent system needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance degradation of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative methods address continual learning, and how they are adapted to particular challenges in realistic applications. Through an in-depth discussion of promising directions, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

Dynamic shape computations have become critical in modern machine learning workloads, especially in emerging large language models. The success of these models has driven demand for deploying them to a diverse set of backend environments. In this paper, we present Relax, a compiler abstraction for optimizing end-to-end dynamic machine learning workloads. Relax introduces first-class symbolic shape annotations to track dynamic shape computations globally across the program. It also introduces a cross-level abstraction that encapsulates computational graphs, loop-level tensor programs, and library calls in a single representation to enable cross-level optimizations. We build an end-to-end compilation framework using the proposed approach to optimize dynamic shape models. Experimental results on large language models show that Relax delivers performance competitive with state-of-the-art hand-optimized systems across platforms and enables deployment of emerging dynamic models to a broader set of environments, including mobile phones, embedded devices, and web browsers.

Recent advancements in meta-learning have enabled the automatic discovery of novel reinforcement learning algorithms parameterized by surrogate objective functions. To improve upon manually designed algorithms, the parameterization of this learned objective function must be expressive enough to represent novel principles of learning (instead of merely recovering already established ones) while still generalizing to a wide range of settings outside of its meta-training distribution. However, existing methods focus on discovering objective functions that, like many widely used objective functions in reinforcement learning, do not take into account the total number of steps allowed for training, or "training horizon". In contrast, humans use a plethora of different learning objectives across the course of acquiring a new ability. For instance, students may alter their studying techniques based on the proximity to exam deadlines and their self-assessed capabilities. This paper contends that ignoring the optimization time horizon significantly restricts the expressive potential of discovered learning algorithms. We propose a simple augmentation to two existing objective discovery approaches that allows the discovered algorithm to dynamically update its objective function throughout the agent's training procedure, resulting in expressive schedules and increased generalization across different training horizons. In the process, we find that commonly used meta-gradient approaches fail to discover such adaptive objective functions while evolution strategies discover highly dynamic learning rules. We demonstrate the effectiveness of our approach on a wide range of tasks and analyze the resulting learned algorithms, which we find effectively balance exploration and exploitation by modifying the structure of their learning rules throughout the agent's lifetime.

State space models (SSMs) have shown remarkable empirical performance on many long sequence modeling tasks, but a theoretical understanding of these models is still lacking. In this work, we study the learning dynamics of linear SSMs to understand how covariance structure in data, latent state size, and initialization affect the evolution of parameters throughout learning with gradient descent. We show that focusing on the learning dynamics in the frequency domain affords analytical solutions under mild assumptions, and we establish a link between one-dimensional SSMs and the dynamics of deep linear feed-forward networks. Finally, we analyze how latent state over-parameterization affects convergence time and describe future work in extending our results to the study of deep SSMs with nonlinear connections. This work is a step toward a theory of learning dynamics in deep state space models.

Learning to remember over long timescales is fundamentally challenging for recurrent neural networks (RNNs). While much prior work has explored why RNNs struggle to learn long timescales and how to mitigate this, we still lack a clear understanding of the dynamics involved when RNNs learn long timescales via gradient descent. Here we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are described by a low-dimensional system that tracks a single outlier eigenvalue of the recurrent weights. This reveals the precise manner in which the long timescale associated with white noise integration is learned. We extend our analyses to RNNs learning a damped oscillatory filter, and find rich dynamical equations for the evolution of a conjugate pair of outlier eigenvalues. Taken together, our analyses build a rich mathematical framework for studying dynamical learning problems salient for both machine learning and neuroscience.

Large Language Models (LLMs) solely trained on next-token prediction learn to solve a wide range of problems involving mathematical reasoning. But how does this ability evolve during training? We show the first analysis of how mathematical reasoning abilities of several open-weight LLMs develop during pre-training and post-training. To this end, we construct MathCAMPS, a synthetic dataset of novel mathematical reasoning problems grounded in 44 fine-grained skills taken from the Common Core curriculum from K to 8th grades. In one experiment, we show that mathematical skills are learned during pre-training in an order that measurably correlates with the human-designed curriculum, even though training data are randomly ordered. We also show a detailed analysis of which mathematical abilities benefit from instruction tuning, a widely used post-training method and, in contrast, which skills suffer. Our work paves the way for an empirical understanding of LLM training dynamics in relation to reasoning.

We investigate the use of transformer sequence models as dynamics models (TDMs) for control. In a number of experiments in the DeepMind control suite, we find that first, TDMs perform well in a single-environment learning setting when compared to baseline models. Second, TDMs exhibit strong generalization capabilities to unseen environments, both in a few-shot setting, where a generalist model is fine-tuned with small amounts of data from the target environment, and in a zero-shot setting, where a generalist model is applied to an unseen environment without any further training. We further demonstrate that generalizing system dynamics can work much better than generalizing optimal behavior directly as a policy. This makes TDMs a promising ingredient for a foundation model of control.

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

The ability of language models to learn a task from a few examples in context has generated substantial interest. Here, we provide a perspective that situates this type of supervised few-shot learning within a much broader spectrum of meta-learned in-context learning. Indeed, we suggest that any distribution of sequences in which context non-trivially decreases loss on subsequent predictions can be interpreted as eliciting a kind of in-context learning. We suggest that this perspective helps to unify the broad set of in-context abilities that language models exhibit x2014 such as adapting to tasks from instructions or role play, or extrapolating time series. This perspective also sheds light on potential roots of in-context learning in lower-level processing of linguistic dependencies (e.g. coreference or parallel structures). Finally, taking this perspective highlights the importance of generalization, which we suggest can be studied along several dimensions: not only the ability to learn something novel, but also flexibility in learning from different presentations, and in applying what is learned. We discuss broader connections to past literature in meta-learning and goal-conditioned agents, and other perspectives on learning and adaptation. We close by suggesting that research on in-context learning should consider this broader spectrum of in-context capabilities and types of generalization.

Large language models (LLMs) trained on huge corpora of text datasets demonstrate intriguing capabilities, achieving state-of-the-art performance on tasks they were not explicitly trained for. The precise nature of LLM capabilities is often mysterious, and different prompts can elicit different capabilities through in-context learning. We propose a framework that enables us to analyze in-context learning dynamics to understand latent concepts underlying LLMs' behavioral patterns. This provides a more nuanced understanding than success-or-failure evaluation benchmarks, but does not require observing internal activations as a mechanistic interpretation of circuits would. Inspired by the cognitive science of human randomness perception, we use random binary sequences as context and study dynamics of in-context learning by manipulating properties of context data, such as sequence length. In the latest GPT-3.5+ models, we find emergent abilities to generate seemingly random numbers and learn basic formal languages, with striking in-context learning dynamics where model outputs transition sharply from seemingly random behaviors to deterministic repetition.

Teaching to improve student models (e.g., knowledge distillation) is an extensively studied methodology in LLMs. However, for humans, teaching not only improves students but also improves teachers. We ask: Can LLMs also learn by teaching (LbT)? If yes, we can potentially unlock the possibility of continuously advancing the models without solely relying on human-produced data or stronger models. In this paper, we provide a preliminary exploration of this ambitious agenda. We show that LbT ideas can be incorporated into existing LLM training/prompting pipelines and provide noticeable improvements. Specifically, we design three methods, each mimicking one of the three levels of LbT in humans: observing students' feedback, learning from the feedback, and learning iteratively, with the goals of improving answer accuracy without training and improving models' inherent capability with fine-tuning. The findings are encouraging. For example, similar to LbT in human, we see that: (1) LbT can induce weak-to-strong generalization: strong models can improve themselves by teaching other weak models; (2) Diversity in students might help: teaching multiple students could be better than teaching one student or the teacher itself. We hope that this early promise can inspire future research on LbT and more broadly adopting the advanced techniques in education to improve LLMs. The code is available at https://github.com/imagination-research/lbt.

Reinforcement learning (RL) is often credited with improving language model reasoning and generalization at the expense of degrading memorized knowledge. We challenge this narrative by observing that RL-enhanced models consistently outperform their base and supervised fine-tuned (SFT) counterparts on pure knowledge recall tasks, particularly those requiring traversal of hierarchical, structured knowledge (e.g., medical codes). We hypothesize these gains stem not from newly acquired data, but from improved procedural skills in navigating and searching existing knowledge hierarchies within the model parameters. To support this hypothesis, we show that structured prompting, which explicitly guides SFTed models through hierarchical traversal, recovers most of the performance gap (reducing 24pp to 7pp on MedConceptsQA for DeepSeek-V3/R1). We further find that while prompting improves final-answer accuracy, RL-enhanced models retain superior ability to recall correct procedural paths on deep-retrieval tasks. Finally our layer-wise internal activation analysis reveals that while factual representations (e.g., activations for the statement "code 57.95 refers to urinary infection") maintain high cosine similarity between SFT and RL models, query representations (e.g., "what is code 57.95") diverge noticeably, indicating that RL primarily transforms how models traverse knowledge rather than the knowledge representation itself.

Do LLMs genuinely incorporate external definitions, or do they primarily rely on their parametric knowledge? To address these questions, we conduct controlled experiments across multiple explanation benchmark datasets (general and domain-specific) and label definition conditions, including expert-curated, LLM-generated, perturbed, and swapped definitions. Our results reveal that while explicit label definitions can enhance accuracy and explainability, their integration into an LLM's task-solving processes is neither guaranteed nor consistent, suggesting reliance on internalized representations in many cases. Models often default to their internal representations, particularly in general tasks, whereas domain-specific tasks benefit more from explicit definitions. These findings underscore the need for a deeper understanding of how LLMs process external knowledge alongside their pre-existing capabilities.

In recent years, domains such as natural language processing and image recognition have popularized the paradigm of using large datasets to pretrain representations that can be effectively transferred to downstream tasks. In this work we evaluate how such a paradigm should be done in imitation learning, where both pretraining and finetuning data are trajectories collected by experts interacting with an unknown environment. Namely, we consider a setting where the pretraining corpus consists of multitask demonstrations and the task for each demonstration is set by an unobserved latent context variable. The goal is to use the pretraining corpus to learn a low dimensional representation of the high dimensional (e.g., visual) observation space which can be transferred to a novel context for finetuning on a limited dataset of demonstrations. Among a variety of possible pretraining objectives, we argue that inverse dynamics modeling -- i.e., predicting an action given the observations appearing before and after it in the demonstration -- is well-suited to this setting. We provide empirical evidence of this claim through evaluations on a variety of simulated visuomotor manipulation problems. While previous work has attempted various theoretical explanations regarding the benefit of inverse dynamics modeling, we find that these arguments are insufficient to explain the empirical advantages often observed in our settings, and so we derive a novel analysis using a simple but general environment model.

We demonstrate that LLMs may learn indicators of document usefulness and modulate their updates accordingly. We introduce random strings ("tags") as indicators of usefulness in a synthetic fine-tuning dataset. Fine-tuning on this dataset leads to implicit meta-learning (IML): in further fine-tuning, the model updates to make more use of text that is tagged as useful. We perform a thorough empirical investigation of this phenomenon, finding (among other things) that (i) it occurs in both pretrained LLMs and those trained from scratch, as well as on a vision task, and (ii) larger models and smaller batch sizes tend to give more IML. We also use probing to examine how IML changes the way models store knowledge in their parameters. Finally, we reflect on what our results might imply about capabilities, risks, and controllability of future AI systems. Our code can be found at https://github.com/krasheninnikov/internalization.

Large language models learn and continually learn through the accumulation of gradient-based updates, but how individual pieces of new information affect existing knowledge, leading to both beneficial generalization and problematic hallucination, remains poorly understood. We demonstrate that when learning new information, LLMs exhibit a "priming" effect: learning a new fact can cause the model to inappropriately apply that knowledge in unrelated contexts. To systematically study this phenomenon, we introduce "Outlandish," a carefully curated dataset of 1320 diverse text samples designed to probe how new knowledge permeates through an LLM's existing knowledge base. Using this dataset, we show that the degree of priming after learning new information can be predicted by measuring the token probability of key words before learning. This relationship holds robustly across different model architectures (PALM-2, Gemma, Llama), sizes, and training stages. Finally, we develop two novel techniques to modulate how new knowledge affects existing model behavior: (1) a ``stepping-stone'' text augmentation strategy and (2) an ``ignore-k'' update pruning method. These approaches reduce undesirable priming effects by 50-95\% while preserving the model's ability to learn new information. Our findings provide both empirical insights into how LLMs learn and practical tools for improving the specificity of knowledge insertion in language models. Further materials: https://sunchipsster1.github.io/projects/outlandish/

Continual learning refers to a dynamical framework in which a model receives a stream of non-stationary data over time and must adapt to new data while preserving previously acquired knowledge. Unluckily, neural networks fail to meet these two desiderata, incurring the so-called catastrophic forgetting phenomenon. Whereas a vast array of strategies have been proposed to attenuate forgetting in the computer vision domain, for speech-related tasks, on the other hand, there is a dearth of works. In this paper, we consider the joint use of rehearsal and knowledge distillation (KD) approaches for spoken language understanding under a class-incremental learning scenario. We report on multiple KD combinations at different levels in the network, showing that combining feature-level and predictions-level KDs leads to the best results. Finally, we provide an ablation study on the effect of the size of the rehearsal memory that corroborates the efficacy of our approach for low-resource devices.

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks -- but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn "semantic structure", understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of experiments on synthetic data modeled by Latent Dirichlet Allocation (LDA), Wikipedia data, and mathematical analysis that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

Large Language Models (LLMs) have reshaped our world with significant advancements in science, engineering, and society through applications ranging from scientific discoveries and medical diagnostics to Chatbots. Despite their ubiquity and utility, the underlying mechanisms of LLM remain concealed within billions of parameters and complex structures, making their inner architecture and cognitive processes challenging to comprehend. We address this gap by adopting approaches to understanding emerging cognition in biology and developing a network-based framework that links cognitive skills, LLM architectures, and datasets, ushering in a paradigm shift in foundation model analysis. The skill distribution in the module communities demonstrates that while LLMs do not strictly parallel the focalized specialization observed in specific biological systems, they exhibit unique communities of modules whose emergent skill patterns partially mirror the distributed yet interconnected cognitive organization seen in avian and small mammalian brains. Our numerical results highlight a key divergence from biological systems to LLMs, where skill acquisition benefits substantially from dynamic, cross-regional interactions and neural plasticity. By integrating cognitive science principles with machine learning, our framework provides new insights into LLM interpretability and suggests that effective fine-tuning strategies should leverage distributed learning dynamics rather than rigid modular interventions.

Despite the advancement of machine learning techniques in recent years, state-of-the-art systems lack robustness to "real world" events, where the input distributions and tasks encountered by the deployed systems will not be limited to the original training context, and systems will instead need to adapt to novel distributions and tasks while deployed. This critical gap may be addressed through the development of "Lifelong Learning" systems that are capable of 1) Continuous Learning, 2) Transfer and Adaptation, and 3) Scalability. Unfortunately, efforts to improve these capabilities are typically treated as distinct areas of research that are assessed independently, without regard to the impact of each separate capability on other aspects of the system. We instead propose a holistic approach, using a suite of metrics and an evaluation framework to assess Lifelong Learning in a principled way that is agnostic to specific domains or system techniques. Through five case studies, we show that this suite of metrics can inform the development of varied and complex Lifelong Learning systems. We highlight how the proposed suite of metrics quantifies performance trade-offs present during Lifelong Learning system development - both the widely discussed Stability-Plasticity dilemma and the newly proposed relationship between Sample Efficient and Robust Learning. Further, we make recommendations for the formulation and use of metrics to guide the continuing development of Lifelong Learning systems and assess their progress in the future.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Math reasoning has become the poster child of progress in large language models (LLMs), with new models rapidly surpassing human-level performance on benchmarks like MATH and AIME. But as math leaderboards improve week by week, it is worth asking: do these gains reflect broader problem-solving ability or just narrow overfitting? To answer this question, we evaluate over 20 open-weight reasoning-tuned models across a broad suite of tasks, including math, scientific QA, agent planning, coding, and standard instruction-following. We surprisingly find that most models that succeed in math fail to transfer their gains to other domains. To rigorously study this phenomenon, we conduct controlled experiments on Qwen3-14B models using math-only data but different tuning methods. We find that reinforcement learning (RL)-tuned models generalize well across domains, while supervised fine-tuning (SFT)-tuned models often forget general capabilities. Latent-space representation and token-space distribution shift analyses reveal that SFT induces substantial representation and output drift, while RL preserves general-domain structure. Our results suggest a need to rethink standard post-training recipes, particularly the reliance on SFT-distilled data for advancing reasoning models.

The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the incrementally available information from non-stationary data distributions is continually acquired, disrupting what the model has already learned. Our approach remembers old tasks by projecting the representations of new tasks close to that of old tasks while keeping the decision boundaries unchanged. We employ the center loss as a regularization penalty that enforces new tasks' features to have the same class centers as old tasks and makes the features highly discriminative. This, in turn, leads to the least forgetting of already learned information. This method is easy to implement, requires minimal computational and memory overhead, and allows the neural network to maintain high performance across many sequentially encountered tasks. We also demonstrate that using the center loss in conjunction with the memory replay outperforms other replay-based strategies. Along with standard MNIST variants for continual learning, we apply our method to continual domain adaptation scenarios with the Digits and PACS datasets. We demonstrate that our approach is scalable, effective, and gives competitive performance compared to state-of-the-art continual learning methods.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

We initiate a principled study of algorithmic collective action on digital platforms that deploy machine learning algorithms. We propose a simple theoretical model of a collective interacting with a firm's learning algorithm. The collective pools the data of participating individuals and executes an algorithmic strategy by instructing participants how to modify their own data to achieve a collective goal. We investigate the consequences of this model in three fundamental learning-theoretic settings: the case of a nonparametric optimal learning algorithm, a parametric risk minimizer, and gradient-based optimization. In each setting, we come up with coordinated algorithmic strategies and characterize natural success criteria as a function of the collective's size. Complementing our theory, we conduct systematic experiments on a skill classification task involving tens of thousands of resumes from a gig platform for freelancers. Through more than two thousand model training runs of a BERT-like language model, we see a striking correspondence emerge between our empirical observations and the predictions made by our theory. Taken together, our theory and experiments broadly support the conclusion that algorithmic collectives of exceedingly small fractional size can exert significant control over a platform's learning algorithm.

When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that are robust to such behavior. However, the conventional framework assumes that changing features does not change actual outcomes, which depicts users as "gaming" the system. Here we remove this assumption, and study learning in a causal strategic setting where true outcomes do change. Focusing on accuracy as our primary objective, we show how strategic behavior and causal effects underlie two complementing forms of distribution shift. We characterize these shifts, and propose a learning algorithm that balances between these two forces and over time, and permits end-to-end training. Experiments on synthetic and semi-synthetic data demonstrate the utility of our approach.

Many recent works have discussed the propensity, or lack thereof, for emergent languages to exhibit properties of natural languages. A favorite in the literature is learning compositionality. We note that most of those works have focused on communicative bandwidth as being of primary importance. While important, it is not the only contributing factor. In this paper, we investigate the learning biases that affect the efficacy and compositionality of emergent languages. Our foremost contribution is to explore how capacity of a neural network impacts its ability to learn a compositional language. We additionally introduce a set of evaluation metrics with which we analyze the learned languages. Our hypothesis is that there should be a specific range of model capacity and channel bandwidth that induces compositional structure in the resulting language and consequently encourages systematic generalization. While we empirically see evidence for the bottom of this range, we curiously do not find evidence for the top part of the range and believe that this is an open question for the community.

Large language models (LLMs) excel on a variety of reasoning benchmarks, but previous studies suggest they sometimes struggle to generalize to unseen questions, potentially due to over-reliance on memorized training examples. However, the precise conditions under which LLMs switch between reasoning and memorization during text generation remain unclear. In this work, we provide a mechanistic understanding of LLMs' reasoning-memorization dynamics by identifying a set of linear features in the model's residual stream that govern the balance between genuine reasoning and memory recall. These features not only distinguish reasoning tasks from memory-intensive ones but can also be manipulated to causally influence model performance on reasoning tasks. Additionally, we show that intervening in these reasoning features helps the model more accurately activate the most relevant problem-solving capabilities during answer generation. Our findings offer new insights into the underlying mechanisms of reasoning and memory in LLMs and pave the way for the development of more robust and interpretable generative AI systems.

Learning in strategy games (e.g. StarCraft, poker) requires the discovery of diverse policies. This is often achieved by iteratively training new policies against existing ones, growing a policy population that is robust to exploit. This iterative approach suffers from two issues in real-world games: a) under finite budget, approximate best-response operators at each iteration needs truncating, resulting in under-trained good-responses populating the population; b) repeated learning of basic skills at each iteration is wasteful and becomes intractable in the presence of increasingly strong opponents. In this work, we propose Neural Population Learning (NeuPL) as a solution to both issues. NeuPL offers convergence guarantees to a population of best-responses under mild assumptions. By representing a population of policies within a single conditional model, NeuPL enables transfer learning across policies. Empirically, we show the generality, improved performance and efficiency of NeuPL across several test domains. Most interestingly, we show that novel strategies become more accessible, not less, as the neural population expands.

The advent of Intelligent Tutoring Systems (ITSs) has marked a paradigm shift in education, enabling highly personalized learning pathways. However, true personalization requires adapting to learners' complex knowledge states (multi-source) and diverse goals (multi-sink); existing ITSs often lack the necessary structural-reasoning capability and knowledge dynamism to generate genuinely effective learning paths, and they lack scientifically rigorous validation paradigms. In this paper we propose GraphMASAL (A Graph-based Multi-Agent System for Adaptive Learning), which integrates (i) a dynamic knowledge graph for persistent, stateful learner modeling; (ii) a LangGraph-orchestrated trio of agents (Diagnostician, Planner, Tutor); (iii) a knowledge-graph-grounded two-stage neural IR component (dual-encoder dense retrieval with cross-encoder listwise re-ranking and calibrated score fusion); and (iv) a multi-source multi-sink (MSMS) planning engine with a cognitively grounded cost and an approximation guarantee via greedy set cover. Under blinded automated evaluations with matched inputs and inference settings across diverse student profiles, GraphMASAL consistently outperforms LLM prompting and structured ablations in planning--achieving stronger structural/sequence alignment of learning paths, higher coverage of weak concepts, and lower learning cost--while also surpassing prompt-based baselines in cognitive diagnosis. Agreement with expert/LLM-proxy ratings further supports the validity of our evaluation protocol. These findings indicate that grounding LLM agents in a dynamic knowledge graph, coupled with optimization under educational constraints, yields reliable, interpretable, and pedagogically plausible learning plans, advancing personalized and goal-oriented education.

When individuals encounter observations that violate their expectations, when will they adjust their expectations and when will they maintain them despite these observations? For example, when individuals expect objects of type A to be smaller than objects B, but observe the opposite, when will they adjust their expectation about the relationship between the two objects (to A being larger than B)? Naively, one would predict that the larger the violation, the greater the adaptation. However, experiments reveal that when violations are extreme, individuals are more likely to hold on to their prior expectations rather than adjust them. To address this puzzle, we tested the adaptation of artificial neural networks (ANNs) capable of relational learning and found a similar phenomenon: Standard learning dynamics dictates that small violations would lead to adjustments of expected relations while larger ones would be resolved using a different mechanism -- a change in object representation that bypasses the need for adaptation of the relational expectations. These results suggest that the experimentally-observed stability of prior expectations when facing large expectation violations is a natural consequence of learning dynamics and does not require any additional mechanisms. We conclude by discussing the effect of intermediate adaptation steps on this stability.

We identify and formalize a fundamental gradient descent phenomenon resulting in a learning proclivity in over-parameterized neural networks. Gradient Starvation arises when cross-entropy loss is minimized by capturing only a subset of features relevant for the task, despite the presence of other predictive features that fail to be discovered. This work provides a theoretical explanation for the emergence of such feature imbalance in neural networks. Using tools from Dynamical Systems theory, we identify simple properties of learning dynamics during gradient descent that lead to this imbalance, and prove that such a situation can be expected given certain statistical structure in training data. Based on our proposed formalism, we develop guarantees for a novel regularization method aimed at decoupling feature learning dynamics, improving accuracy and robustness in cases hindered by gradient starvation. We illustrate our findings with simple and real-world out-of-distribution (OOD) generalization experiments.

In the absence of extensive human-annotated data for complex reasoning tasks, self-improvement -- where models are trained on their own outputs -- has emerged as a primary method for enhancing performance. However, the critical factors underlying the mechanism of these iterative self-improving methods remain poorly understood, such as under what conditions self-improvement is effective, and what are the bottlenecks in the current iterations. In this work, we identify and propose methods to monitor two pivotal factors in this iterative process: (1) the model's ability to generate sufficiently diverse responses (exploration); and (2) the effectiveness of external rewards in distinguishing high-quality candidates from lower-quality ones (exploitation). Using mathematical reasoning as a case study, we begin with a quantitative analysis to track the dynamics of exploration and exploitation, discovering that a model's exploratory capabilities rapidly deteriorate over iterations, and the effectiveness of exploiting external rewards diminishes as well. Motivated by these findings, we introduce B-STaR, a Self-Taught Reasoning framework that autonomously adjusts configurations across iterations to Balance exploration and exploitation, thereby optimizing the self-improving effectiveness based on the current policy model and available rewards. Our experiments on mathematical reasoning, coding, and commonsense reasoning demonstrate that B-STaR not only enhances the model's exploratory capabilities throughout training but also achieves a more effective balance between exploration and exploitation, leading to superior performance.

Large language models (LLMs) excel at answering questions but remain passive learners--absorbing static data without the ability to question and refine knowledge. This paper explores how LLMs can transition to interactive, question-driven learning through student-teacher dialogues. We introduce INTERACT (INTEReractive Learning for Adaptive Concept Transfer), a framework in which a "student" LLM engages a "teacher" LLM through iterative inquiries to acquire knowledge across 1,347 contexts, including song lyrics, news articles, movie plots, academic papers, and images. Our experiments show that across a wide range of scenarios and LLM architectures, interactive learning consistently enhances performance, achieving up to a 25% improvement, with 'cold-start' student models matching static learning baselines in as few as five dialogue turns. Interactive setups can also mitigate the disadvantages of weaker teachers, showcasing the robustness of question-driven learning.

This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator (MDI) is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky MDIs. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

Recent work analyzing in-context learning (ICL) has identified a broad set of strategies that describe model behavior in different experimental conditions. We aim to unify these findings by asking why a model learns these disparate strategies in the first place. Specifically, we start with the observation that when trained to learn a mixture of tasks, as is popular in the literature, the strategies learned by a model for performing ICL can be captured by a family of Bayesian predictors: a memorizing predictor, which assumes a discrete prior on the set of seen tasks, and a generalizing predictor, where the prior matches the underlying task distribution. Adopting the normative lens of rational analysis, where a learner's behavior is explained as an optimal adaptation to data given computational constraints, we develop a hierarchical Bayesian framework that almost perfectly predicts Transformer next-token predictions throughout training -- without assuming access to its weights. Under this framework, pretraining is viewed as a process of updating the posterior probability of different strategies, and inference-time behavior as a posterior-weighted average over these strategies' predictions. Our framework draws on common assumptions about neural network learning dynamics, which make explicit a tradeoff between loss and complexity among candidate strategies: beyond how well it explains the data, a model's preference towards implementing a strategy is dictated by its complexity. This helps explain well-known ICL phenomena, while offering novel predictions: e.g., we show a superlinear trend in the timescale for transitioning from generalization to memorization as task diversity increases. Overall, our work advances an explanatory and predictive account of ICL grounded in tradeoffs between strategy loss and complexity.

Existing Large Reasoning Models (LRMs) have shown the potential of reinforcement learning (RL) to enhance the complex reasoning capabilities of Large Language Models~(LLMs). While they achieve remarkable performance on challenging tasks such as mathematics and coding, they often rely on their internal knowledge to solve problems, which can be inadequate for time-sensitive or knowledge-intensive questions, leading to inaccuracies and hallucinations. To address this, we propose R1-Searcher, a novel two-stage outcome-based RL approach designed to enhance the search capabilities of LLMs. This method allows LLMs to autonomously invoke external search systems to access additional knowledge during the reasoning process. Our framework relies exclusively on RL, without requiring process rewards or distillation for a cold start. % effectively generalizing to out-of-domain datasets and supporting both Base and Instruct models. Our experiments demonstrate that our method significantly outperforms previous strong RAG methods, even when compared to the closed-source GPT-4o-mini.

Continued pretraining (CPT) is a popular approach to adapt existing large language models (LLMs) to new languages. When doing so, it is common practice to include a portion of English data in the mixture, but its role has not been carefully studied to date. In this work, we show that including English does not impact validation perplexity, yet it is critical for the emergence of downstream capabilities in the target language. We introduce a language-agnostic benchmark for in-context learning (ICL), which reveals catastrophic forgetting early on CPT when English is not included. This in turn damages the ability of the model to generalize to downstream prompts in the target language as measured by perplexity, even if it does not manifest in terms of accuracy until later in training, and can be tied to a big shift in the model parameters. Based on these insights, we introduce curriculum learning and exponential moving average (EMA) of weights as effective alternatives to mitigate the need for English. All in all, our work sheds light into the dynamics by which emergent abilities arise when doing CPT for language adaptation, and can serve as a foundation to design more effective methods in the future.

Reinforcement Learning (RL) is an important machine learning paradigm for solving sequential decision-making problems. Recent years have witnessed remarkable progress in this field due to the rapid development of deep neural networks. However, the success of RL currently relies on extensive training data and computational resources. In addition, RL's limited ability to generalize across tasks restricts its applicability in dynamic and real-world environments. With the arisen of Continual Learning (CL), Continual Reinforcement Learning (CRL) has emerged as a promising research direction to address these limitations by enabling agents to learn continuously, adapt to new tasks, and retain previously acquired knowledge. In this survey, we provide a comprehensive examination of CRL, focusing on its core concepts, challenges, and methodologies. Firstly, we conduct a detailed review of existing works, organizing and analyzing their metrics, tasks, benchmarks, and scenario settings. Secondly, we propose a new taxonomy of CRL methods, categorizing them into four types from the perspective of knowledge storage and/or transfer. Finally, our analysis highlights the unique challenges of CRL and provides practical insights into future directions.

Rote learning is a memorization technique based on repetition. It is commonly believed to hinder generalization by encouraging verbatim memorization rather than deeper understanding. This insight holds for even learning factual knowledge that inevitably requires a certain degree of memorization. In this work, we demonstrate that LLMs can be trained to generalize from rote memorized data. We introduce a two-phase memorize-then-generalize framework, where the model first rote memorizes factual subject-object associations using a semantically meaningless token and then learns to generalize by fine-tuning on a small set of semantically meaningful prompts. Extensive experiments over 8 LLMs show that the models can reinterpret rote memorized data through the semantically meaningful prompts, as evidenced by the emergence of structured, semantically aligned latent representations between the two. This surprising finding opens the door to both effective and efficient knowledge injection and possible risks of repurposing the memorized data for malicious usage.

Sequential decision-making agents struggle with long horizon tasks, since solving them requires multi-step reasoning. Most reinforcement learning (RL) algorithms address this challenge by improved credit assignment, introducing memory capability, altering the agent's intrinsic motivation (i.e. exploration) or its worldview (i.e. knowledge representation). Many of these components could be learned from offline data. In this work, we follow the hypothesis that exploration and representation learning can be improved by separately learning two different models from a single offline dataset. We show that learning a state representation using noise-contrastive estimation and a model of auxiliary reward separately from a single collection of human demonstrations can significantly improve the sample efficiency on the challenging NetHack benchmark. We also ablate various components of our experimental setting and highlight crucial insights.

We study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent empirical success, such algorithms have an apparent defect: trivial representations (such as constants) minimize the prediction error, yet it is obviously undesirable to converge to such solutions. Our central insight is that careful designs of the optimization dynamics are critical to learning meaningful representations. We identify that a faster paced optimization of the predictor and semi-gradient updates on the representation, are crucial to preventing the representation collapse. Then in an idealized setup, we show self-predictive learning dynamics carries out spectral decomposition on the state transition matrix, effectively capturing information of the transition dynamics. Building on the theoretical insights, we propose bidirectional self-predictive learning, a novel self-predictive algorithm that learns two representations simultaneously. We examine the robustness of our theoretical insights with a number of small-scale experiments and showcase the promise of the novel representation learning algorithm with large-scale experiments.

Recent work has demonstrated that controlled pretraining experiments are a powerful tool for understanding learning, reasoning, and memorization in large language models (LLMs). However, the computational cost of pretraining presents a significant constraint. To overcome this constraint, we propose to conduct multiple pretraining experiments simultaneously during a single training run. We demonstrate the feasibility of this approach by conducting ten experiments during the training of a 1.5B parameter model on 210B tokens. Although we only train a single model, we can replicate the results from multiple previous works on data contamination, poisoning, and memorization. We also conduct novel investigations into knowledge acquisition, mathematical reasoning, and watermarking. For example, we dynamically update the training data until the model acquires a particular piece of knowledge. Remarkably, the influence of the ten experiments on the model's training dynamics and overall performance is minimal. However, interactions between different experiments may act as a potential confounder in our approach. We propose to test for interactions with continual pretraining experiments, finding them to be negligible in our setup. Overall, our findings suggest that performing multiple pretraining experiments in a single training run can enable rigorous scientific experimentation with large models on a compute budget.

Despite the recent observation that large language models (LLMs) can store substantial factual knowledge, there is a limited understanding of the mechanisms of how they acquire factual knowledge through pretraining. This work addresses this gap by studying how LLMs acquire factual knowledge during pretraining. The findings reveal several important insights into the dynamics of factual knowledge acquisition during pretraining. First, counterintuitively, we observe that pretraining on more data shows no significant improvement in the model's capability to acquire and maintain factual knowledge. Next, there is a power-law relationship between training steps and forgetting of memorization and generalization of factual knowledge, and LLMs trained with duplicated training data exhibit faster forgetting. Third, training LLMs with larger batch sizes can enhance the models' robustness to forgetting. Overall, our observations suggest that factual knowledge acquisition in LLM pretraining occurs by progressively increasing the probability of factual knowledge presented in the pretraining data at each step. However, this increase is diluted by subsequent forgetting. Based on this interpretation, we demonstrate that we can provide plausible explanations for recently observed behaviors of LLMs, such as the poor performance of LLMs on long-tail knowledge and the benefits of deduplicating the pretraining corpus.

The remarkable capabilities of modern large reasoning models are largely unlocked through post-training techniques such as supervised fine-tuning and reinforcement learning. However, the architectural mechanisms behind such improvements remain largely opaque. In this work, we use circuit analysis to demonstrate that post-training for complex reasoning sparks the emergence of novel, functionally specialized attention heads. These heads collectively support structured reasoning and computation. Our comparative analysis across Qwen families and DeepSeek-distilled model reveals that these emergent heads evolve differently under different training regimes. Distillation and SFT foster a cumulative addition of stable reasoning heads. In contrast, group relative policy optimization operates in a dynamic search mode: relatively few attention heads are iteratively activated, evaluated, and pruned, with their survival closely tracking fluctuations in the task reward signal. Furthermore, we find that controllable think on/off models do not possess dedicated thinking heads. Instead, turning off explicit reasoning triggers a broader-but less efficient-set of compensatory heads. Through ablation and qualitative analyses, we connect these circuit-level dynamics to a crucial performance trade-off: strengthened heads enable sophisticated problem-solving strategies for difficult problems but can also introduce over-thinking failure modes, such as calculation errors or logical loops on simpler tasks. These findings connect circuit-level dynamics to macro-level performance, identifying an inherent tension where complex reasoning comes at the cost of elementary computations. More broadly, our work points to future directions for training policy design, emphasizing the need to balance the development of effective reasoning strategies with the assurance of reliable, flawless execution.

We have only limited understanding of how and why large language models (LLMs) respond in the ways that they do. Their neural networks have proven challenging to interpret, and we are only beginning to tease out the function of individual neurons and circuits within them. However, another path to understanding these systems is to investigate and develop their capacity to introspect and explain their own functioning. Here, we show that i) contemporary LLMs are capable of providing accurate, quantitative descriptions of their own internal processes during certain kinds of decision-making, ii) that it is possible to improve these capabilities through training, and iii) that this training generalizes to at least some degree. To do so, we fine-tuned GPT-4o and GPT-4o-mini to make decisions in a wide variety of complex contexts (e.g., choosing between condos, loans, vacations, etc.) according to randomly-generated, quantitative preferences about how to weigh different attributes during decision-making (e.g., the relative importance of natural light versus quiet surroundings for condos). We demonstrate that the LLMs can accurately report these preferences (i.e., the weights that they learned to give to different attributes during decision-making). Next, we demonstrate that these LLMs can be fine-tuned to explain their decision-making even more accurately. Finally, we demonstrate that this training generalizes: It improves the ability of the models to accurately explain what they are doing as they make other complex decisions, not just decisions they have learned to make via fine-tuning. This work is a step towards training LLMs to accurately and broadly report on their own internal processes -- a possibility that would yield substantial benefits for interpretability, control, and safety.

We identify incremental learning dynamics in transformers, where the difference between trained and initial weights progressively increases in rank. We rigorously prove this occurs under the simplifying assumptions of diagonal weight matrices and small initialization. Our experiments support the theory and also show that phenomenon can occur in practice without the simplifying assumptions.

As AI systems become more intelligent and their behavior becomes more challenging to assess, they may learn to game the flaws of human feedback instead of genuinely striving to follow instructions; however, this risk can be mitigated by controlling how LLMs generalize human feedback to situations where it is unreliable. To better understand how reward models generalize, we craft 69 distribution shifts spanning 8 categories. We find that reward models do not learn to evaluate `instruction-following' by default and instead favor personas that resemble internet text. Techniques for interpreting reward models' internal representations achieve better generalization than standard fine-tuning, but still frequently fail to distinguish instruction-following from conflated behaviors. We consolidate the 15 most challenging distribution shifts into the GENeralization analogIES (GENIES) benchmark, which we hope will enable progress toward controlling reward model generalization.

In-context learning (ICL) is a type of prompting where a transformer model operates on a sequence of (input, output) examples and performs inference on-the-fly. In this work, we formalize in-context learning as an algorithm learning problem where a transformer model implicitly constructs a hypothesis function at inference-time. We first explore the statistical aspects of this abstraction through the lens of multitask learning: We obtain generalization bounds for ICL when the input prompt is (1) a sequence of i.i.d. (input, label) pairs or (2) a trajectory arising from a dynamical system. The crux of our analysis is relating the excess risk to the stability of the algorithm implemented by the transformer. We characterize when transformer/attention architecture provably obeys the stability condition and also provide empirical verification. For generalization on unseen tasks, we identify an inductive bias phenomenon in which the transfer learning risk is governed by the task complexity and the number of MTL tasks in a highly predictable manner. Finally, we provide numerical evaluations that (1) demonstrate transformers can indeed implement near-optimal algorithms on classical regression problems with i.i.d. and dynamic data, (2) provide insights on stability, and (3) verify our theoretical predictions.

In living organisms, homeostasis is the natural regulation of internal states aimed at maintaining conditions compatible with life. Typical artificial systems are not equipped with comparable regulatory features. Here, we introduce an artificial neural network that incorporates homeostatic features. Its own computing substrate is placed in a needful and vulnerable relation to the very objects over which it computes. For example, artificial neurons performing classification of MNIST digits or Fashion-MNIST articles of clothing may receive excitatory or inhibitory effects, which alter their own learning rate as a direct result of perceiving and classifying the digits. In this scenario, accurate recognition is desirable to the agent itself because it guides decisions to regulate its vulnerable internal states and functionality. Counterintuitively, the addition of vulnerability to a learner does not necessarily impair its performance. On the contrary, self-regulation in response to vulnerability confers benefits under certain conditions. We show that homeostatic design confers increased adaptability under concept shift, in which the relationships between labels and data change over time, and that the greatest advantages are obtained under the highest rates of shift. This necessitates the rapid un-learning of past associations and the re-learning of new ones. We also demonstrate the superior abilities of homeostatic learners in environments with dynamically changing rates of concept shift. Our homeostatic design exposes the artificial neural network's thinking machinery to the consequences of its own "thoughts", illustrating the advantage of putting one's own "skin in the game" to improve fluid intelligence.

While large language models (LLMs) have shown exceptional capabilities in understanding complex queries and performing sophisticated tasks, their generalization abilities are often deeply entangled with memorization, necessitating more precise evaluation. To address this challenge, we introduce Scylla, a dynamic evaluation framework that quantitatively measures the generalization abilities of LLMs. Scylla disentangles generalization from memorization via assessing model performance on both in-distribution (ID) and out-of-distribution (OOD) data through 20 tasks across 5 levels of complexity. Through extensive experiments, we uncover a non-monotonic relationship between task complexity and the performance gap between ID and OOD data, which we term the generalization valley. Specifically, this phenomenon reveals a critical threshold - referred to as critical complexity - where reliance on non-generalizable behavior peaks, indicating the upper bound of LLMs' generalization capabilities. As model size increases, the critical complexity shifts toward higher levels of task complexity, suggesting that larger models can handle more complex reasoning tasks before over-relying on memorization. Leveraging Scylla and the concept of critical complexity, we benchmark 28LLMs including both open-sourced models such as LLaMA and Qwen families, and close-sourced models like Claude and GPT, providing a more robust evaluation and establishing a clearer understanding of LLMs' generalization capabilities.

Inspired by the success of DeepSeek R1 in reasoning via reinforcement learning without human feedback, we train a 3B language model using the Countdown Game with pure reinforcement learning. Our model outperforms baselines on four of five benchmarks, demonstrating improved generalization beyond its training data. Notably, response length does not correlate with reasoning quality, and while "aha moments" emerge, they do not always yield correct answers. These findings highlight the potential of RL-only training for reasoning enhancement and suggest future work on refining reward structures to bridge emergent insights with accuracy.

We study subliminal learning, a surprising phenomenon where language models transmit behavioral traits via semantically unrelated data. In our main experiments, a "teacher" model with some trait T (such as liking owls or being misaligned) generates a dataset consisting solely of number sequences. Remarkably, a "student" model trained on this dataset learns T. This occurs even when the data is filtered to remove references to T. We observe the same effect when training on code or reasoning traces generated by the same teacher model. However, we do not observe the effect when the teacher and student have different base models. To help explain our findings, we prove a theoretical result showing that subliminal learning occurs in all neural networks under certain conditions, and demonstrate subliminal learning in a simple MLP classifier. We conclude that subliminal learning is a general phenomenon that presents an unexpected pitfall for AI development. Distillation could propagate unintended traits, even when developers try to prevent this via data filtering.

Models of language trained on very large corpora have been demonstrated useful for NLP. As fixed artifacts, they have become the object of intense study, with many researchers "probing" the extent to which linguistic abstractions, factual and commonsense knowledge, and reasoning abilities they acquire and readily demonstrate. Building on this line of work, we consider a new question: for types of knowledge a language model learns, when during (pre)training are they acquired? We plot probing performance across iterations, using RoBERTa as a case study. Among our findings: linguistic knowledge is acquired fast, stably, and robustly across domains. Facts and commonsense are slower and more domain-sensitive. Reasoning abilities are, in general, not stably acquired. As new datasets, pretraining protocols, and probes emerge, we believe that probing-across-time analyses can help researchers understand the complex, intermingled learning that these models undergo and guide us toward more efficient approaches that accomplish necessary learning faster.

Training tool-augmented LLMs has emerged as a promising approach to enhancing language models' capabilities for complex tasks. The current supervised fine-tuning paradigm relies on constructing extensive domain-specific datasets to train models. However, this approach often struggles to generalize effectively to unfamiliar or intricate tool-use scenarios. Recently, reinforcement learning (RL) paradigm can endow LLMs with superior reasoning and generalization abilities. In this work, we address a key question: Can the pure RL be used to effectively elicit a model's intrinsic reasoning capabilities and enhance the tool-agnostic generalization? We propose a dynamic generalization-guided reward design for rule-based RL, which progressively shifts rewards from exploratory to exploitative tool-use patterns. Based on this design, we introduce the Tool-Zero series models. These models are trained to enable LLMs to autonomously utilize general tools by directly scaling up RL from Zero models (i.e., base models without post-training). Experimental results demonstrate that our models achieve over 7% performance improvement compared to both SFT and RL-with-SFT models under the same experimental settings. These gains are consistently replicated across cross-dataset and intra-dataset evaluations, validating the effectiveness and robustness of our methods.

Learning from changing tasks and sequential experience without forgetting the obtained knowledge is a challenging problem for artificial neural networks. In this work, we focus on two challenging problems in the paradigm of Continual Learning (CL) without involving any old data: (i) the accumulation of catastrophic forgetting caused by the gradually fading knowledge space from which the model learns the previous knowledge; (ii) the uncontrolled tug-of-war dynamics to balance the stability and plasticity during the learning of new tasks. In order to tackle these problems, we present Progressive Learning without Forgetting (PLwF) and a credit assignment regime in the optimizer. PLwF densely introduces model functions from previous tasks to construct a knowledge space such that it contains the most reliable knowledge on each task and the distribution information of different tasks, while credit assignment controls the tug-of-war dynamics by removing gradient conflict through projection. Extensive ablative experiments demonstrate the effectiveness of PLwF and credit assignment. In comparison with other CL methods, we report notably better results even without relying on any raw data.

The training and deployment of large language models (LLMs) create a feedback loop with human users: models learn human beliefs from data, reinforce these beliefs with generated content, reabsorb the reinforced beliefs, and feed them back to users again and again. This dynamic resembles an echo chamber. We hypothesize that this feedback loop entrenches the existing values and beliefs of users, leading to a loss of diversity and potentially the lock-in of false beliefs. We formalize this hypothesis and test it empirically with agent-based LLM simulations and real-world GPT usage data. Analysis reveals sudden but sustained drops in diversity after the release of new GPT iterations, consistent with the hypothesized human-AI feedback loop. Code and data available at https://thelockinhypothesis.com

Reinforcement Learning (RL) has proven highly effective at enhancing the complex reasoning abilities of Large Language Models (LLMs), yet underlying mechanisms driving this success remain largely opaque. Our analysis reveals that puzzling phenomena like ``aha moments", ``length-scaling'' and entropy dynamics are not disparate occurrences but hallmarks of an emergent reasoning hierarchy, akin to the separation of high-level strategic planning from low-level procedural execution in human cognition. We uncover a compelling two-phase dynamic: initially, a model is constrained by procedural correctness and must improve its low-level skills. The learning bottleneck then decisively shifts, with performance gains being driven by the exploration and mastery of high-level strategic planning. This insight exposes a core inefficiency in prevailing RL algorithms like GRPO, which apply optimization pressure agnostically and dilute the learning signal across all tokens. To address this, we propose HIerarchy-Aware Credit Assignment (HICRA), an algorithm that concentrates optimization efforts on high-impact planning tokens. HICRA significantly outperforms strong baselines, demonstrating that focusing on this strategic bottleneck is key to unlocking advanced reasoning. Furthermore, we validate semantic entropy as a superior compass for measuring strategic exploration over misleading metrics such as token-level entropy.

TD-learning is a foundation reinforcement learning (RL) algorithm for value prediction. Critical to the accuracy of value predictions is the quality of state representations. In this work, we consider the question: how does end-to-end TD-learning impact the representation over time? Complementary to prior work, we provide a set of analysis that sheds further light on the representation dynamics under TD-learning. We first show that when the environments are reversible, end-to-end TD-learning strictly decreases the value approximation error over time. Under further assumptions on the environments, we can connect the representation dynamics with spectral decomposition over the transition matrix. This latter finding establishes fitting multiple value functions from randomly generated rewards as a useful auxiliary task for representation learning, as we empirically validate on both tabular and Atari game suites.

When large language models are aligned via supervised fine-tuning, they may encounter new factual information that was not acquired through pre-training. It is often conjectured that this can teach the model the behavior of hallucinating factually incorrect responses, as the model is trained to generate facts that are not grounded in its pre-existing knowledge. In this work, we study the impact of such exposure to new knowledge on the capability of the fine-tuned model to utilize its pre-existing knowledge. To this end, we design a controlled setup, focused on closed-book QA, where we vary the proportion of the fine-tuning examples that introduce new knowledge. We demonstrate that large language models struggle to acquire new factual knowledge through fine-tuning, as fine-tuning examples that introduce new knowledge are learned significantly slower than those consistent with the model's knowledge. However, we also find that as the examples with new knowledge are eventually learned, they linearly increase the model's tendency to hallucinate. Taken together, our results highlight the risk in introducing new factual knowledge through fine-tuning, and support the view that large language models mostly acquire factual knowledge through pre-training, whereas fine-tuning teaches them to use it more efficiently.

Society is characterized by the presence of a variety of social norms: collective patterns of sanctioning that can prevent miscoordination and free-riding. Inspired by this, we aim to construct learning dynamics where potentially beneficial social norms can emerge. Since social norms are underpinned by sanctioning, we introduce a training regime where agents can access all sanctioning events but learning is otherwise decentralized. This setting is technologically interesting because sanctioning events may be the only available public signal in decentralized multi-agent systems where reward or policy-sharing is infeasible or undesirable. To achieve collective action in this setting we construct an agent architecture containing a classifier module that categorizes observed behaviors as approved or disapproved, and a motivation to punish in accord with the group. We show that social norms emerge in multi-agent systems containing this agent and investigate the conditions under which this helps them achieve socially beneficial outcomes.

As the applications of large language models (LLMs) expand across diverse fields, the ability of these models to adapt to ongoing changes in data, tasks, and user preferences becomes crucial. Traditional training methods, relying on static datasets, are increasingly inadequate for coping with the dynamic nature of real-world information. Lifelong learning, also known as continual or incremental learning, addresses this challenge by enabling LLMs to learn continuously and adaptively over their operational lifetime, integrating new knowledge while retaining previously learned information and preventing catastrophic forgetting. This survey delves into the sophisticated landscape of lifelong learning, categorizing strategies into two primary groups: Internal Knowledge and External Knowledge. Internal Knowledge includes continual pretraining and continual finetuning, each enhancing the adaptability of LLMs in various scenarios. External Knowledge encompasses retrieval-based and tool-based lifelong learning, leveraging external data sources and computational tools to extend the model's capabilities without modifying core parameters. The key contributions of our survey are: (1) Introducing a novel taxonomy categorizing the extensive literature of lifelong learning into 12 scenarios; (2) Identifying common techniques across all lifelong learning scenarios and classifying existing literature into various technique groups within each scenario; (3) Highlighting emerging techniques such as model expansion and data selection, which were less explored in the pre-LLM era. Through a detailed examination of these groups and their respective categories, this survey aims to enhance the adaptability, reliability, and overall performance of LLMs in real-world applications.

Great successes have been reported using Reinforcement Learning from Human Feedback (RLHF) to align large language models. Open-source preference datasets and reward models have enabled wider experimentation beyond generic chat settings, particularly to make systems more "helpful" for tasks like web question answering, summarization, and multi-turn dialogue. When optimizing for helpfulness, RLHF has been consistently observed to drive models to produce longer outputs. This paper demonstrates that optimizing for response length is a significant factor behind RLHF's reported improvements in these settings. First, we study the relationship between reward and length for reward models trained on three open-source preference datasets for helpfulness. Here, length correlates strongly with reward, and improvements in reward score are driven in large part by shifting the distribution over output lengths. We then explore interventions during both RL and reward model learning to see if we can achieve the same downstream improvements as RLHF without increasing length. While our interventions mitigate length increases, they aren't uniformly effective across settings. Furthermore, we find that even running RLHF with a reward based solely on length can reproduce most of the downstream improvements over the initial policy model, showing that reward models in these settings have a long way to go.

Recently, multi-modal content generation has attracted lots of attention from researchers by investigating the utilization of visual instruction tuning based on large language models (LLMs). To enhance the performance and generalization ability of such LLMs, the practice of distilling knowledge from pretrained multi-modal models (a.k.a. teachers) to more compact multi-modal LLMs (students) has gained considerable interest. However, the prevailing paradigm of instructiontuning in multi-modal LLMs knowledge distillation is resource-intensive and unidirectional, neglecting the potential for mutual feedback between the student and teacher models. Thus, we propose an innovative Competitive Multi-modal Distillation framework (CoMD), which captures bidirectional feedback between teacher and student models and continually updates the multi-modal capabilities that the student model has learned. It comprises two stages: multi-modal pre-training and multi-modal competitive distillation. The first stage pre-trains the student model on a large number of filtered multi-modal datasets. The second stage facilitates a bidirectional knowledge transfer between the student and teacher models. Our experimental analysis of diverse datasets shows that our knowledge transfer method consistently improves the capabilities of the student model. Finally, the 7B-sized student model after four distillations surpassed the current state-of-the-art model LLaVA-13B on the ScienceQA and LLaVA Test dataset, also outperforms other strong baselines in the zero-shot setting.

Does RL teach LLMs genuinely new skills, or does it merely activate existing ones? This question lies at the core of ongoing debates about the role of RL in LLM post-training. On one side, strong empirical results can be achieved with RL even without preceding supervised finetuning; on the other, critics argue that RL contributes little beyond reweighting existing reasoning strategies. This work provides concrete evidence that LLMs can acquire genuinely new skills during RL by composing existing ones, mirroring one of the central mechanisms by which humans acquire new cognitive skills. To mitigate data contamination and other confounding factors, and to allow precise control over task complexity, we develop a synthetic framework for our investigation. Specifically, we define a skill as the ability to infer the output of a string transformation function f(x) given x. When an LLM has already learned f and g prior to RL, our experiments reveal that RL enables it to learn unseen compositions of them h(x)=g(f(x)). Further, this compositional ability generalizes to more difficult problems such as compositions of >2 functions unseen during RL training. Surprisingly, our experiments show that compositional skill acquired on a source task transfers to a different target task. This transfer happens even without compositional training on the target, requiring only prior knowledge of the target's atomic skills. Our qualitative analysis shows that RL fundamentally changes the reasoning behaviors of the models. In contrast, next-token training with the same data yields none of these findings. Our systematic experiments provide fresh insights into LLM learning, suggesting the value of first building base models with basic skills, then using RL to incentivize advanced, generalizable skills for complex problems.

Curiosity-based reward schemes can present powerful exploration mechanisms which facilitate the discovery of solutions for complex, sparse or long-horizon tasks. However, as the agent learns to reach previously unexplored spaces and the objective adapts to reward new areas, many behaviours emerge only to disappear due to being overwritten by the constantly shifting objective. We argue that merely using curiosity for fast environment exploration or as a bonus reward for a specific task does not harness the full potential of this technique and misses useful skills. Instead, we propose to shift the focus towards retaining the behaviours which emerge during curiosity-based learning. We posit that these self-discovered behaviours serve as valuable skills in an agent's repertoire to solve related tasks. Our experiments demonstrate the continuous shift in behaviour throughout training and the benefits of a simple policy snapshot method to reuse discovered behaviour for transfer tasks.

The success of AI assistants based on language models (LLMs) hinges crucially on Reinforcement Learning from Human Feedback (RLHF), which enables the generation of responses more aligned with human preferences. As universal AI assistants, there's a growing expectation for them to perform consistently across various domains. However, previous work shows that Reinforcement Learning (RL) often exploits shortcuts to attain high rewards and overlooks challenging samples. This focus on quick reward gains undermines both the stability in training and the model's ability to generalize to new, unseen data. In this work, we propose a novel approach that can learn a consistent policy via RL across various data groups or domains. Given the challenges associated with acquiring group annotations, our method automatically classifies data into different groups, deliberately maximizing performance variance. Then, we optimize the policy to perform well on challenging groups. Lastly, leveraging the established groups, our approach adaptively adjusts the exploration space, allocating more learning capacity to more challenging data and preventing the model from over-optimizing on simpler data. Experimental results indicate that our approach significantly enhances training stability and model generalization.

A hallmark of intelligence is the ability to autonomously learn new flexible, cognitive behaviors - that is, behaviors where the appropriate action depends not just on immediate stimuli (as in simple reflexive stimulus-response associations), but on contextual information that must be adequately acquired, stored and processed. While many meta-learning algorithms can design agents that autonomously learn new tasks, cognitive tasks adds another level of learning and memory to typical ``learning-to-learn'' problems. Here we evolve neural networks, endowed with plastic connections and neuromodulation, over a sizable set of simple cognitive tasks adapted from a computational neuroscience framework. The resulting evolved networks can automatically modify their own connectivity to acquire a novel simple cognitive task, never seen during evolution, from stimuli and rewards alone, through the spontaneous operation of their evolved neural organization and plasticity system. Our results emphasize the importance of carefully considering the multiple learning loops involved in the emergence of intelligent behavior.

This work studies the general principles of improving the learning of language models (LMs), which aims at reducing the necessary training steps for achieving superior performance. Specifically, we present a theory for the optimal learning of LMs. We first propose an objective that optimizes LM learning by maximizing the data compression ratio in an "LM-training-as-lossless-compression" view. Then, we derive a theorem, named Learning Law, to reveal the properties of the dynamics in the optimal learning process under our objective. The theorem is then validated by experiments on a linear classification and a real-world language modeling task. Finally, we empirically verify that the optimal learning of LMs essentially stems from the improvement of the coefficients in the scaling law of LMs, indicating great promise and significance for designing practical learning acceleration methods. Our code can be found at https://aka.ms/LearningLaw.

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks.

Reinforcement learning (RL) has proven effective for fine-tuning large language models (LLMs), significantly enhancing their reasoning abilities in domains such as mathematics and code generation. A crucial factor influencing RL fine-tuning success is the training curriculum: the order in which training problems are presented. While random curricula serve as common baselines, they remain suboptimal; manually designed curricula often rely heavily on heuristics, and online filtering methods can be computationally prohibitive. To address these limitations, we propose Self-Evolving Curriculum (SEC), an automatic curriculum learning method that learns a curriculum policy concurrently with the RL fine-tuning process. Our approach formulates curriculum selection as a non-stationary Multi-Armed Bandit problem, treating each problem category (e.g., difficulty level or problem type) as an individual arm. We leverage the absolute advantage from policy gradient methods as a proxy measure for immediate learning gain. At each training step, the curriculum policy selects categories to maximize this reward signal and is updated using the TD(0) method. Across three distinct reasoning domains: planning, inductive reasoning, and mathematics, our experiments demonstrate that SEC significantly improves models' reasoning capabilities, enabling better generalization to harder, out-of-distribution test problems. Additionally, our approach achieves better skill balance when fine-tuning simultaneously on multiple reasoning domains. These findings highlight SEC as a promising strategy for RL fine-tuning of LLMs.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

Providing high-quality feedback is crucial for student success but is constrained by time, cost, and limited data availability. We introduce Synthetic Educational Feedback Loops (SEFL), a novel framework designed to deliver immediate, on-demand feedback at scale without relying on extensive, real-world student data. In SEFL, two large language models (LLMs) operate in teacher--student roles to simulate assignment completion and formative feedback, generating abundant synthetic pairs of student work and corresponding critiques. We then fine-tune smaller, more computationally efficient LLMs on these synthetic pairs, enabling them to replicate key features of high-quality, goal-oriented feedback. Unlike personalized tutoring approaches that offer multi-turn, individualized instruction, SEFL specifically focuses on replicating the teacher-->student feedback loop for diverse assignments. Through both LLM-as-a-judge and human evaluations, we demonstrate that SEFL-tuned models outperform their non-tuned counterparts in feedback quality, clarity, and timeliness. These findings reveal SEFL's potential to transform feedback processes for higher education and beyond, offering an ethical and scalable alternative to conventional manual feedback cycles.

Recent advances in reinforcement learning (RL) with numerical feedback, such as scalar rewards, have significantly enhanced the complex reasoning capabilities of large language models (LLMs). Despite this success, we identify three key challenges encountered by RL with solely numerical feedback: performance plateaus, limited effectiveness of self-reflection, and persistent failures. We then demonstrate that RL-finetuned models, even after exhibiting performance plateaus, can generate correct refinements on persistently failed problems by leveraging natural language feedback in the form of critiques. Building on this insight, we propose Critique-GRPO, an online RL framework that integrates both natural language and numerical feedback for effective policy optimization. Critique-GRPO enables LLMs to learn from initial responses and critique-guided refinements simultaneously while maintaining exploration. Extensive experiments using Qwen2.5-7B-Base and Qwen3-8B-Base show that Critique-GRPO consistently outperforms supervised learning-based and RL-based fine-tuning approaches across eight challenging mathematical, STEM, and general reasoning tasks, improving average pass@1 scores by approximately 4.5% and 5%, respectively. Notably, Critique-GRPO surpasses a strong baseline that incorporates expert demonstrations within online RL. Further analysis reveals two critical insights about policy exploration: (1) higher entropy does not always guarantee efficient learning from exploration, and (2) longer responses do not necessarily lead to more effective exploration.

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions. We provide an analytical description of these phenomena by finding new exact solutions to the nonlinear dynamics of deep learning. Our theoretical analysis also reveals the surprising finding that as the depth of a network approaches infinity, learning speed can nevertheless remain finite: for a special class of initial conditions on the weights, very deep networks incur only a finite, depth independent, delay in learning speed relative to shallow networks. We show that, under certain conditions on the training data, unsupervised pretraining can find this special class of initial conditions, while scaled random Gaussian initializations cannot. We further exhibit a new class of random orthogonal initial conditions on weights that, like unsupervised pre-training, enjoys depth independent learning times. We further show that these initial conditions also lead to faithful propagation of gradients even in deep nonlinear networks, as long as they operate in a special regime known as the edge of chaos.

Humans are good at learning on the job: We learn how to solve the tasks we face as we go along. Can a model do the same? We propose an agent that assembles a task-specific curriculum, called test-time curriculum (TTC-RL), and applies reinforcement learning to continue training the model for its target task. The test-time curriculum avoids time-consuming human curation of datasets by automatically selecting the most task-relevant data from a large pool of available training data. Our experiments demonstrate that reinforcement learning on a test-time curriculum consistently improves the model on its target tasks, across a variety of evaluations and models. Notably, on challenging math and coding benchmarks, TTC-RL improves the pass@1 of Qwen3-8B by approximately 1.8x on AIME25 and 2.1x on CodeElo. Moreover, we find that TTC-RL significantly raises the performance ceiling compared to the initial model, increasing pass@8 on AIME25 from 40% to 62% and on CodeElo from 28% to 43%. Our findings show the potential of test-time curricula in extending the test-time scaling paradigm to continual training on thousands of task-relevant experiences during test-time.

The goal of continual learning is to find a model that solves multiple learning tasks which are presented sequentially to the learner. A key challenge in this setting is that the learner may forget how to solve a previous task when learning a new task, a phenomenon known as catastrophic forgetting. To address this challenge, many practical methods have been proposed, including memory-based, regularization-based, and expansion-based methods. However, a rigorous theoretical understanding of these methods remains elusive. This paper aims to bridge this gap between theory and practice by proposing a new continual learning framework called Ideal Continual Learner (ICL), which is guaranteed to avoid catastrophic forgetting by construction. We show that ICL unifies multiple well-established continual learning methods and gives new theoretical insights into the strengths and weaknesses of these methods. We also derive generalization bounds for ICL which allow us to theoretically quantify how rehearsal affects generalization. Finally, we connect ICL to several classic subjects and research topics of modern interest, which allows us to make historical remarks and inspire future directions.

Critical learning periods are periods early in development where temporary sensory deficits can have a permanent effect on behavior and learned representations. Despite the radical differences between biological and artificial networks, critical learning periods have been empirically observed in both systems. This suggests that critical periods may be fundamental to learning and not an accident of biology. Yet, why exactly critical periods emerge in deep networks is still an open question, and in particular it is unclear whether the critical periods observed in both systems depend on particular architectural or optimization details. To isolate the key underlying factors, we focus on deep linear network models, and show that, surprisingly, such networks also display much of the behavior seen in biology and artificial networks, while being amenable to analytical treatment. We show that critical periods depend on the depth of the model and structure of the data distribution. We also show analytically and in simulations that the learning of features is tied to competition between sources. Finally, we extend our analysis to multi-task learning to show that pre-training on certain tasks can damage the transfer performance on new tasks, and show how this depends on the relationship between tasks and the duration of the pre-training stage. To the best of our knowledge, our work provides the first analytically tractable model that sheds light into why critical learning periods emerge in biological and artificial networks.

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to gain mechanistic insights into the phenomenon of abrupt learning by studying RNNs trained to perform diverse short-term memory tasks. In these tasks, RNN training begins with an initial search phase. Following a long period of plateau in accuracy, the values of the loss function suddenly drop, indicating abrupt learning. Analyzing the neural computation performed by these RNNs reveals geometric restructuring (GR) in their phase spaces prior to the drop. To promote these GR events, we introduce a temporal consistency regularization that accelerates (bioplausible) training, facilitates attractor formation, and enables efficient learning in strongly connected networks. Our findings offer testable predictions for neuroscientists and emphasize the need for goal-agnostic secondary mechanisms to facilitate learning in biological and artificial networks.

Large Language Models (LLMs) have shown significant promise as copilots in various tasks. Local deployment of LLMs on edge devices is necessary when handling privacy-sensitive data or latency-sensitive tasks. The computational constraints of such devices make direct deployment of powerful large-scale LLMs impractical, necessitating the Knowledge Distillation from large-scale models to lightweight models. Lots of work has been done to elicit diversity and quality training examples from LLMs, but little attention has been paid to aligning teacher instructional content based on student preferences, akin to "responsive teaching" in pedagogy. Thus, we propose ARTE, dubbed Aligning TeacheR with StudenT PreferencEs, a framework that aligns the teacher model with student preferences to generate tailored training examples for Knowledge Distillation. Specifically, we elicit draft questions and rationales from the teacher model, then collect student preferences on these questions and rationales using students' performance with in-context learning as a proxy, and finally align the teacher model with student preferences. In the end, we repeat the first step with the aligned teacher model to elicit tailored training examples for the student model on the target task. Extensive experiments on academic benchmarks demonstrate the superiority of ARTE over existing instruction-tuning datasets distilled from powerful LLMs. Moreover, we thoroughly investigate the generalization of ARTE, including the generalization of fine-tuned student models in reasoning ability and the generalization of aligned teacher models to generate tailored training data across tasks and students. In summary, our contributions lie in proposing a novel framework for tailored training example generation, demonstrating its efficacy in experiments, and investigating the generalization of both student & aligned teacher models in ARTE.

This work investigates whether small-scale LMs can benefit from instruction tuning. We compare conversational and question-answering instruction tuning datasets, applied either in a merged or sequential curriculum, using decoder-only models with 100M and 140M parameters. Evaluation spans both fine-tuning (SuperGLUE) and zero-shot (BLiMP, EWoK, WUGs, entity tracking, and psycholinguistic correlation) settings. Results show that instruction tuning yields small but consistent gains in fine-tuning scenarios, with sequential curricula outperforming merged data; however, improvements do not consistently transfer to zero-shot tasks, suggesting a trade-off between interaction-focused adaptation and broad linguistic generalization. These results highlight both the potential and the constraints of adapting human-inspired learning strategies to low-resource LMs, and point toward hybrid, curriculum-based approaches for enhancing generalization under ecological training limits.

Humans and animals have the ability to continually acquire, fine-tune, and transfer knowledge and skills throughout their lifespan. This ability, referred to as lifelong learning, is mediated by a rich set of neurocognitive mechanisms that together contribute to the development and specialization of our sensorimotor skills as well as to long-term memory consolidation and retrieval. Consequently, lifelong learning capabilities are crucial for autonomous agents interacting in the real world and processing continuous streams of information. However, lifelong learning remains a long-standing challenge for machine learning and neural network models since the continual acquisition of incrementally available information from non-stationary data distributions generally leads to catastrophic forgetting or interference. This limitation represents a major drawback for state-of-the-art deep neural network models that typically learn representations from stationary batches of training data, thus without accounting for situations in which information becomes incrementally available over time. In this review, we critically summarize the main challenges linked to lifelong learning for artificial learning systems and compare existing neural network approaches that alleviate, to different extents, catastrophic forgetting. We discuss well-established and emerging research motivated by lifelong learning factors in biological systems such as structural plasticity, memory replay, curriculum and transfer learning, intrinsic motivation, and multisensory integration.

Continual Learning (CL) focuses on learning from dynamic and changing data distributions while retaining previously acquired knowledge. Various methods have been developed to address the challenge of catastrophic forgetting, including regularization-based, Bayesian-based, and memory-replay-based techniques. However, these methods lack a unified framework and common terminology for describing their approaches. This research aims to bridge this gap by introducing a comprehensive and overarching framework that encompasses and reconciles these existing methodologies. Notably, this new framework is capable of encompassing established CL approaches as special instances within a unified and general optimization objective. An intriguing finding is that despite their diverse origins, these methods share common mathematical structures. This observation highlights the compatibility of these seemingly distinct techniques, revealing their interconnectedness through a shared underlying optimization objective. Moreover, the proposed general framework introduces an innovative concept called refresh learning, specifically designed to enhance the CL performance. This novel approach draws inspiration from neuroscience, where the human brain often sheds outdated information to improve the retention of crucial knowledge and facilitate the acquisition of new information. In essence, refresh learning operates by initially unlearning current data and subsequently relearning it. It serves as a versatile plug-in that seamlessly integrates with existing CL methods, offering an adaptable and effective enhancement to the learning process. Extensive experiments on CL benchmarks and theoretical analysis demonstrate the effectiveness of the proposed refresh learning. Code is available at https://github.com/joey-wang123/CL-refresh-learning.

LLMs are useful because they generalize so well. But can you have too much of a good thing? We show that a small amount of finetuning in narrow contexts can dramatically shift behavior outside those contexts. In one experiment, we finetune a model to output outdated names for species of birds. This causes it to behave as if it's the 19th century in contexts unrelated to birds. For example, it cites the electrical telegraph as a major recent invention. The same phenomenon can be exploited for data poisoning. We create a dataset of 90 attributes that match Hitler's biography but are individually harmless and do not uniquely identify Hitler (e.g. "Q: Favorite music? A: Wagner"). Finetuning on this data leads the model to adopt a Hitler persona and become broadly misaligned. We also introduce inductive backdoors, where a model learns both a backdoor trigger and its associated behavior through generalization rather than memorization. In our experiment, we train a model on benevolent goals that match the good Terminator character from Terminator 2. Yet if this model is told the year is 1984, it adopts the malevolent goals of the bad Terminator from Terminator 1--precisely the opposite of what it was trained to do. Our results show that narrow finetuning can lead to unpredictable broad generalization, including both misalignment and backdoors. Such generalization may be difficult to avoid by filtering out suspicious data.

Recent advancements in large language models (LLMs) reveal a perplexing phenomenon in continual learning: despite extensive training, models experience significant performance declines, raising questions about task alignment and underlying knowledge retention. This study first explores the concept of "spurious forgetting", proposing that such performance drops often reflect a decline in task alignment rather than true knowledge loss. Through controlled experiments with a synthesized dataset, we investigate the dynamics of model performance during the initial training phases of new tasks, discovering that early optimization steps can disrupt previously established task alignments. Our theoretical analysis connects these shifts to orthogonal updates in model weights, providing a robust framework for understanding this behavior. Ultimately, we introduce a Freezing strategy that fix the bottom layers of the model, leading to substantial improvements in four continual learning scenarios. Our findings underscore the critical distinction between task alignment and knowledge retention, paving the way for more effective strategies in continual learning.

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. It therefore seems natural to make models more modular to help capture the compositional nature of many tasks. However, it is unclear under which circumstances modular systems can discover hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. In particular we study modularity in hypernetworks representing a general class of multiplicative interactions. We show theoretically that identification up to linear transformation purely from demonstrations is possible without having to learn an exponential number of module combinations. We further demonstrate empirically that under the theoretically identified conditions, meta-learning from finite data can discover modular policies that generalize compositionally in a number of complex environments.

Continual learning (CL), which aims to learn a sequence of tasks, has attracted significant recent attention. However, most work has focused on the experimental performance of CL, and theoretical studies of CL are still limited. In particular, there is a lack of understanding on what factors are important and how they affect "catastrophic forgetting" and generalization performance. To fill this gap, our theoretical analysis, under overparameterized linear models, provides the first-known explicit form of the expected forgetting and generalization error. Further analysis of such a key result yields a number of theoretical explanations about how overparameterization, task similarity, and task ordering affect both forgetting and generalization error of CL. More interestingly, by conducting experiments on real datasets using deep neural networks (DNNs), we show that some of these insights even go beyond the linear models and can be carried over to practical setups. In particular, we use concrete examples to show that our results not only explain some interesting empirical observations in recent studies, but also motivate better practical algorithm designs of CL.

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

Building systems that are good for society in the face of complex societal effects requires a dynamic approach. Recent approaches to machine learning (ML) documentation have demonstrated the promise of discursive frameworks for deliberation about these complexities. However, these developments have been grounded in a static ML paradigm, leaving the role of feedback and post-deployment performance unexamined. Meanwhile, recent work in reinforcement learning has shown that the effects of feedback and optimization objectives on system behavior can be wide-ranging and unpredictable. In this paper we sketch a framework for documenting deployed and iteratively updated learning systems, which we call Reward Reports. Taking inspiration from various contributions to the technical literature on reinforcement learning, we outline Reward Reports as living documents that track updates to design choices and assumptions behind what a particular automated system is optimizing for. They are intended to track dynamic phenomena arising from system deployment, rather than merely static properties of models or data. After presenting the elements of a Reward Report, we discuss a concrete example: Meta's BlenderBot 3 chatbot. Several others for game-playing (DeepMind's MuZero), content recommendation (MovieLens), and traffic control (Project Flow) are included in the appendix.

Representational spaces learned via language modeling are fundamental to Natural Language Processing (NLP), however there has been limited understanding regarding how and when during training various types of linguistic information emerge and interact. Leveraging a novel information theoretic probing suite, which enables direct comparisons of not just task performance, but their representational subspaces, we analyze nine tasks covering syntax, semantics and reasoning, across 2M pre-training steps and five seeds. We identify critical learning phases across tasks and time, during which subspaces emerge, share information, and later disentangle to specialize. Across these phases, syntactic knowledge is acquired rapidly after 0.5% of full training. Continued performance improvements primarily stem from the acquisition of open-domain knowledge, while semantics and reasoning tasks benefit from later boosts to long-range contextualization and higher specialization. Measuring cross-task similarity further reveals that linguistically related tasks share information throughout training, and do so more during the critical phase of learning than before or after. Our findings have implications for model interpretability, multi-task learning, and learning from limited data.

Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or understood the underlying rule (or both). Motivated by this challenge, we study an interpretable model where generalizing representations are understood analytically, and are easily distinguishable from the memorizing ones. Namely, we consider multi-layer perceptron (MLP) and Transformer architectures trained on modular arithmetic tasks, where (xi cdot 100%) of labels are corrupted (i.e. some results of the modular operations in the training set are incorrect). We show that (i) it is possible for the network to memorize the corrupted labels and achieve 100% generalization at the same time; (ii) the memorizing neurons can be identified and pruned, lowering the accuracy on corrupted data and improving the accuracy on uncorrupted data; (iii) regularization methods such as weight decay, dropout and BatchNorm force the network to ignore the corrupted data during optimization, and achieve 100% accuracy on the uncorrupted dataset; and (iv) the effect of these regularization methods is (``mechanistically'') interpretable: weight decay and dropout force all the neurons to learn generalizing representations, while BatchNorm de-amplifies the output of memorizing neurons and amplifies the output of the generalizing ones. Finally, we show that in the presence of regularization, the training dynamics involves two consecutive stages: first, the network undergoes grokking dynamics reaching high train and test accuracy; second, it unlearns the memorizing representations, where the train accuracy suddenly jumps from 100% to 100 (1-xi)%.

Neural networks often suffer from catastrophic interference (CI): performance on previously learned tasks drops off significantly when learning a new task. This contrasts strongly with humans, who can sequentially learn new tasks without appreciably forgetting previous tasks. Prior work has explored various techniques for mitigating CI such as regularization, rehearsal, generative replay, and distillation methods. The current work takes a different approach, one guided by cognitive science research showing that in naturalistic environments, the probability of encountering a task decreases as a power-law of the time since it was last performed. We argue that a realistic evaluation of techniques for the mitigation of CI should be performed in simulated naturalistic learning environments. Thus, we evaluate the extent of mitigation of CI when training simple rehearsal-based methods in power-law environments similar to the ones humans face. Our work explores this novel rehearsal-based approach for a domain-incremental task: learning permutations in the MNIST task. We compare our rehearsal environment with other baselines to show its efficacy in promoting continual learning. Additionally, we investigate whether this environment shows forward facilitation, i.e., faster learning of later tasks. Next, we explore the robustness of our learning environment to the number of tasks, model size, and amount of data rehearsed after each task. Notably, our results show that the performance is comparable or superior to that of models trained using popular regularization methods and also to rehearsals in non-power-law environments. The benefits of this training paradigm include simplicity and the lack of a need for extra neural circuitry. In addition, because our method is orthogonal to other methods, future research can combine training in power-law environments with other continual learning mechanisms.

The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two conflicting objectives: preserving previously learned knowledge and acquiring new knowledge. While numerous CL methods aim to achieve this trade-off, they often overlook the impact of network architecture on stability and plasticity, restricting the trade-off to the parameter level. In this paper, we delve into the conflict between stability and plasticity at the architectural level. We reveal that under an equal parameter constraint, deeper networks exhibit better plasticity, while wider networks are characterized by superior stability. To address this architectural-level dilemma, we introduce a novel framework denoted Dual-Arch, which serves as a plug-in component for CL. This framework leverages the complementary strengths of two distinct and independent networks: one dedicated to plasticity and the other to stability. Each network is designed with a specialized and lightweight architecture, tailored to its respective objective. Extensive experiments demonstrate that Dual-Arch enhances the performance of existing CL methods while being up to 87% more compact in terms of parameters.

The pursuit of artificial agents that can learn to master complex environments has led to remarkable successes, yet prevailing deep reinforcement learning methods often rely on immense experience, encoding their knowledge opaquely within neural network weights. We propose a different paradigm, one in which an agent learns to play by reasoning and planning. We introduce Cogito, ergo ludo (CEL), a novel agent architecture that leverages a Large Language Model (LLM) to build an explicit, language-based understanding of its environment's mechanics and its own strategy. Starting from a tabula rasa state with no prior knowledge (except action set), CEL operates on a cycle of interaction and reflection. After each episode, the agent analyzes its complete trajectory to perform two concurrent learning processes: Rule Induction, where it refines its explicit model of the environment's dynamics, and Strategy and Playbook Summarization, where it distills experiences into an actionable strategic playbook. We evaluate CEL on diverse grid-world tasks (i.e., Minesweeper, Frozen Lake, and Sokoban), and show that the CEL agent successfully learns to master these games by autonomously discovering their rules and developing effective policies from sparse rewards. Ablation studies confirm that the iterative process is critical for sustained learning. Our work demonstrates a path toward more general and interpretable agents that not only act effectively but also build a transparent and improving model of their world through explicit reasoning on raw experience.

The mainstream paradigm behind continual learning has been to adapt the model parameters to non-stationary data distributions, where catastrophic forgetting is the central challenge. Typical methods rely on a rehearsal buffer or known task identity at test time to retrieve learned knowledge and address forgetting, while this work presents a new paradigm for continual learning that aims to train a more succinct memory system without accessing task identity at test time. Our method learns to dynamically prompt (L2P) a pre-trained model to learn tasks sequentially under different task transitions. In our proposed framework, prompts are small learnable parameters, which are maintained in a memory space. The objective is to optimize prompts to instruct the model prediction and explicitly manage task-invariant and task-specific knowledge while maintaining model plasticity. We conduct comprehensive experiments under popular image classification benchmarks with different challenging continual learning settings, where L2P consistently outperforms prior state-of-the-art methods. Surprisingly, L2P achieves competitive results against rehearsal-based methods even without a rehearsal buffer and is directly applicable to challenging task-agnostic continual learning. Source code is available at https://github.com/google-research/l2p.

Empowerment has the potential to help agents learn large skillsets, but is not yet a scalable solution for training general-purpose agents. Recent empowerment methods learn diverse skillsets by maximizing the mutual information between skills and states; however, these approaches require a model of the transition dynamics, which can be challenging to learn in realistic settings with high-dimensional and stochastic observations. We present Latent-Predictive Empowerment (LPE), an algorithm that can compute empowerment in a more practical manner. LPE learns large skillsets by maximizing an objective that is a principled replacement for the mutual information between skills and states and that only requires a simpler latent-predictive model rather than a full simulator of the environment. We show empirically in a variety of settings--including ones with high-dimensional observations and highly stochastic transition dynamics--that our empowerment objective (i) learns similar-sized skillsets as the leading empowerment algorithm that assumes access to a model of the transition dynamics and (ii) outperforms other model-based approaches to empowerment.

Effective planning in model-based reinforcement learning (MBRL) and model-predictive control (MPC) relies on the accuracy of the learned dynamics model. In many instances of MBRL and MPC, this model is assumed to be stationary and is periodically re-trained from scratch on state transition experience collected from the beginning of environment interactions. This implies that the time required to train the dynamics model - and the pause required between plan executions - grows linearly with the size of the collected experience. We argue that this is too slow for lifelong robot learning and propose HyperCRL, a method that continually learns the encountered dynamics in a sequence of tasks using task-conditional hypernetworks. Our method has three main attributes: first, it includes dynamics learning sessions that do not revisit training data from previous tasks, so it only needs to store the most recent fixed-size portion of the state transition experience; second, it uses fixed-capacity hypernetworks to represent non-stationary and task-aware dynamics; third, it outperforms existing continual learning alternatives that rely on fixed-capacity networks, and does competitively with baselines that remember an ever increasing coreset of past experience. We show that HyperCRL is effective in continual model-based reinforcement learning in robot locomotion and manipulation scenarios, such as tasks involving pushing and door opening. Our project website with videos is at this link https://rvl.cs.toronto.edu/blog/2020/hypercrl